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IMA Newsletter #379

May 2008

2007-2008 Program

Mathematics of Molecular and Cellular Biology

See http://www.ima.umn.edu/2007-2008 for a full description of the 2007-2008 program on Mathematics of Molecular and Cellular Biology.

The 2008 IMA Summer Program Geometrical Singularities and Singular Geometries, July 14-25, 2008, will focus on the interplay between geometry and physics in the material world through the study of singular stuctures.

This two week workshop at the IMA, organized by L. Mahadevan, Engineering and Applied Sciences, Harvard University, Edward A. Spiegel, Astronomy, Columbia University, Thomas A. Witten, Physics, University of Chicago, and Wendy Zhang, Physics, University of Chicago, will focus on what we know and what we would like to know about these types of singular structures; with the first week focusing on fluid singularities, and the second on elastic singularities. We also expect to have an intense mid-week mini-tutorial on singularities in geometric field theories: examples from gravitation to condensed matter.

Complex Fluids and Complex Flows: The preliminary program for the IMA Thematic year 2009-2010 on Complex Fluids and Complex Flows is now available on line.

IMA Events

IMA Workshop

Stochastic Models for Intracellular Reaction Networks

May 11-13, 2008

Organizers: Gheorghe Craciun (University of Wisconsin), Thomas G. Kurtz (University of Wisconsin), Lea Popovic (Concordia University), Grzegorz A. Rempala (University of Louisville), Ruth J. Williams (University of California, San Diego), John Yin (University of Wisconsin)

IMA Annual Program Year Workshop

Quantitative Approaches to Cell Motility and Chemotaxis

May 27-30, 2008

Organizers: Robert Bourret (University of North Carolina), Alex Mogilner (University of California), Julie A. Theriot (Stanford University)

Thursday, May 1

2:00p-3:00pPrescribing thermal forcing for physical systemsPeter R. Kramer (Rensselaer Polytechnic Institute)Lind Hall 409 WS-STM

Tuesday, May 6

11:15a-12:15pA model for transfer phenomena in structured populationsPeter Hinow (University of Minnesota)Lind Hall 409 PS

Wednesday, May 7

11:15a-12:15pModeling the genome-wide transient response to stimuli in yeast: adaptation through integral feedbackClaudio Altafini (International School for Advanced Studies (SISSA/ISAS))Lind Hall 409 MMCB

Sunday, May 11

All DayIntroductory lectures SW5.11-13.08
12:00p-1:00pRegistration and coffeeEE/CS 3-176 SW5.11-13.08
1:00p-1:15pWelcome and introductionChehrzad Shakiban (University of Minnesota)EE/CS 3-180 SW5.11-13.08
1:15p-2:15pOpening plenary talk: Stochastic analysis is the fundamental tool for understanding biological function Michael C. Reed (Duke University)EE/CS 3-180 SW5.11-13.08
2:15p-2:30pCoffeeEE/CS 3-176 SW5.11-13.08
2:30p-3:30pModels and measures of virus growth and infection spreadJohn Yin (University of Wisconsin)EE/CS 3-180 SW5.11-13.08
3:30p-4:00pCoffeeEE/CS 3-176 SW5.11-13.08
4:00p-5:00pAnalyzing stochastic models Thomas G. Kurtz (University of Wisconsin)EE/CS 3-180 SW5.11-13.08
5:00p-5:30pSecond chancesEE/CS 3-180 SW5.11-13.08
6:30p-8:30pWorkshop dinnerCaspian Bistro
2418 University Ave SE Minneapolis, MN 55414

Monday, May 12

8:30a-9:00aCoffee EE/CS 3-176 SW5.11-13.08
9:00a-10:00aSubdiffusion and reaction networks in biophysicsSamuel Kou (Harvard University)EE/CS 3-180 SW5.11-13.08
10:00a-10:30aCoffeeEE/CS 3-176 SW5.11-13.08
10:30a-11:30aFundamental limits on the suppression of randomness in biologyJohan Paulsson (Harvard Medical School)EE/CS 3-180 SW5.11-13.08
11:30a-1:15pLunchEE/CS 3-176 SW5.11-13.08
1:15p-2:45pAn introduction to discrete-event simulationPeter W. Glynn (Stanford University)
Peter J. Haas (IBM Research Division)
EE/CS 3-180 SW5.11-13.08
2:45p-3:15pCoffeeEE/CS 3-176 SW5.11-13.08
3:15p-3:45pPart I: Local and global stability of biochemical reaction network dynamics Gheorghe Craciun (University of Wisconsin)EE/CS 3-180 SW5.11-13.08
3:50p-4:20pPart II: Homotopy methods for counting reaction network equilibriaRuth J. Williams (University of California, San Diego)EE/CS 3-180 SW5.11-13.08
4:20p-4:50pSecond chancesEE/CS 3-180 SW5.11-13.08
4:50p-5:00pGroup photo SW5.11-13.08
5:00p-6:30pReception and Poster SessionLind Hall 400 SW5.11-13.08
Product form stationary distributions for deficiency zero chemical reaction networks David F. Anderson (University of Wisconsin)
Solutions to inverse problems of biochemical networks using stochastic methods Mónica F. Bugallo (SUNY)
Petar M. Djuric (SUNY)
Interlaced Euler scheme for stiff stochastic differential equationsIoana Cipcigan (University of Maryland Baltimore County)
Muruhan Rathinam (University of Maryland Baltimore County)
Stochastic simulations of reaction-diffusion modelsAnilkumar Devarapu (University of Louisville)
Simulating discrete biochemical reaction systemsArnab Ganguly (University of Wisconsin)
Multiscale methods in a heat shock response model Hye-Won Kang (University of Wisconsin)
Stochastic models for intracellular reaction networksYiannis N. Kaznessis (University of Minnesota)
Stochastic control analysis for biological reaction systemsKyung Hyuk Kim (University of Washington)
Predicting translation rate from sequenceHoward Salis (University of California)
Stochastic modeling of vesicular stomatitis virus(VSV) growth in cells: An application of order statistics to predict replication delaysRishi Srivastava (University of Wisconsin)
Stochastic modeling of bistable chemical systems: Schlogl's modelMelissa Vellela (University of Washington)
Biochemical and network modeling of the mammalian suprachiasmatic nucleus Richard Yamada (University of Michigan)

Tuesday, May 13

8:15a-8:45aCoffeeEE/CS 3-176 SW5.11-13.08
8:45a-9:45aStochastic oscillations in small genetic networksLev S. Tsimring (University of California, San Diego)EE/CS 3-180 SW5.11-13.08
9:45a-10:45aMultiscale models for synthetic biologyYiannis N. Kaznessis (University of Minnesota)EE/CS 3-180 SW5.11-13.08
10:45a-11:15aCoffeeEE/CS 3-176 SW5.11-13.08
11:15a-12:15p Stochastic aspects of actin filament dynamics Hans G. Othmer (University of Minnesota)EE/CS 3-180 SW5.11-13.08
12:15p-1:45pLunchEE/CS 3-180 SW5.11-13.08
1:45p-2:45pBayesian inference for stochastic intracellular reaction network modelsDarren James Wilkinson (University of Newcastle upon Tyne)EE/CS 3-180 SW5.11-13.08
2:45p-3:45pInferring an underlying reaction network from the dataGrzegorz A. Rempala (University of Louisville)EE/CS 3-180 SW5.11-13.08
3:45p-4:15pCoffeeEE/CS 3-176 SW5.11-13.08
4:15p-4:45pSecond chancesEE/CS 3-180 SW5.11-13.08
4:45p-5:45pClosing plenary talk: Metabolic engineering and metabolic modeling: where do we go from here? James C. Liao (University of California)EE/CS 3-180 SW5.11-13.08

Wednesday, May 14

11:15a-12:15pSome mathematical issues arising in single and multiple target SELEXHoward A. Levine (Iowa State University)Lind Hall 409 MMCB

Thursday, May 15

2:00p-3:00pTheoretical framework for microscopic osmotic phenomenaPeter R. Kramer (Rensselaer Polytechnic Institute)Lind Hall 409 WS-STM

Tuesday, May 20

11:15a-12:15pThe cohesin ring is required for centrosome integrityDuncan J. Clarke (University of Minnesota)Lind Hall 409 PS

Wednesday, May 21

11:15a-12:15pAnomalous diffusion, tumor growth and random walk modelsSergei Fedotov (University of Manchester)Lind Hall 409 MMCB

Thursday, May 22

2:00p-3:00pClassification of solution to a nonlinear biharmonic equation with negative exponentYung-Sze Choi (University of Connecticut)Lind Hall 409

Monday, May 26

All DayMemorial Day. The IMA is closed.

Tuesday, May 27

8:15a-9:00aRegistration and coffeeEE/CS 3-176 W5.27-30.08
9:00a-9:15aWelcome to the IMADouglas N. Arnold (University of Minnesota)EE/CS 3-180 W5.27-30.08
9:15a-10:05aActin and a-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor independent mannerRick Horwitz (University of Virginia)EE/CS 3-180 W5.27-30.08
10:05a-10:35aCoffeeEE/CS 3-176 W5.27-30.08
10:35a-11:25aModular control model for endothelial sheet migration Tobias Meyer (Stanford University)EE/CS 3-180 W5.27-30.08
11:25a-2:00aLunch W5.27-30.08
2:00p-2:50pNew methods to study motile phenomenaKen Jacobson (University of North Carolina)EE/CS 3-180 W5.27-30.08
2:50p-3:05pGroup Photo W5.27-30.08
3:05p-3:35pCoffeeEE/CS 3-176 W5.27-30.08
3:35p-4:25pActin organization at the cell edge: mechanism for formation of lamellipodium -lamellum interfaceMichael M. Kozlov (Tel Aviv University)EE/CS 3-180 W5.27-30.08
4:30p-6:30pReception and Poster SessionLind Hall 400 W5.27-30.08
A robustly wrong Listeria motility model, and its redemptionJonathan B. Alberts (University of Washington)
A stochastic immersed boundary method incorporating thermal fluctuations: Coarse-grained micromechanicsPaul Atzberger (University of California)
Dynamic contractile F-actin cortex during cell shape change and morphogenesisLance Davidson (University of Pittsburgh)
Intracellular polarization of motile cells Adriana Dawes (University of Washington)
Cell motility as persistent random motion: theories from experimentsHenrik Flyvbjerg (Technical University of Denmark)
F-actin dynamics regulate force transmission at focal adhesionsMargaret Gardel (University of Chicago)
Microtubule assembly dynamics at the nanoscaleMelissa K. Gardner (University of Minnesota)
Coupling the cytoskeleton to the membrane: driving dynamic cellular shape transitionsNir Shachna Gov (Weizmann Institute of Science)
Dynamic multivariate analysis of single cell motility Mark Harris (Vanderbilt University)
Eric Kim (Vanderbilt University)
Mathematical and computational tools for cell-mechanobiologyDirk Hartmann (Ruprecht-Karls-Universität Heidelberg)
Simulation of concentration-dependent contraction of cellPilhwa Lee (University of Colorado)
Model for protein concentration gradients in the cytoplasmKaren Lipkow (University of Cambridge)
David Odde (University of Minnesota)
Smoldyn, a novel simulator for cellular systems biology Karen Lipkow (University of Cambridge)
Quantitative analysis of stream formation during dictyostelium chemotaxisWolfgang Losert (University of Maryland)
Cellular dynamics simulations of MCF-10A cell random migration in 2-D Alka A. Potdar (Vanderbilt University)
Modeling cell rheology: microrheology of viscoelastic networksSebastian Ambrose Sandersius (Arizona State University)
A continuum model of the cytoskeleton dynamics in lamellipodiaChristian Schmeiser (Universität Wien)
Tenascin-C is upregulated at the end of the cell cycle in proliferating NIH 3T3 fibroblastsBenjamin L. Stottrup (Augsburg College)
Spatiotemporal modelling of intracellular signalling in Rhodobacter sphaeroidessMarcus John Tindall (University of Oxford)
Chemotaxis of E. coli towards glucoseRajitha Vuppula (Indian Institute of Technology-Bombay)
Automated characterization of cell shape changes during amoeboid motilityYuan Xiong (Johns Hopkins University)
The minimal molecular surface Shan Zhao (University of Alabama)
A Multiscale model of endothelial cell migration, proliferation and maturation in angiogenesis Xiaoming Zheng (University of Michigan)
From the curve straightening flow in the plane to a model for the Lamellipodial Actin-cytoskeletonDietmar Bernhard Ölz (Universität Wien)

Wednesday, May 28

8:30a-9:00aCoffeeEE/CS 3-176 W5.27-30.08
9:00a-9:50aComputational modeling of invadopodia-ECM interactions Alissa Weaver (Vanderbilt University)EE/CS 3-180 W5.27-30.08
9:55a-10:45aEffects of nonequilibrium processes on actin dynamics and force generationAnders E. Carlsson (Washington University)EE/CS 3-180 W5.27-30.08
10:45a-11:15aCoffeeEE/CS 3-176 W5.27-30.08
11:15a-12:05pDevelopmental regulation of cell motilityDenise Montell (Johns Hopkins University)EE/CS 3-180 W5.27-30.08
12:05p-2:00pLunch W5.27-30.08
2:00p-2:50pAdherent cells as a mechanical device - probing the forces and understanding the regulatory circuitYu-li Wang (University of Massachusetts Medical School, Worcester Campus)EE/CS 3-180 W5.27-30.08
2:55p-3:45pAnalysis of actin FLAP dynamics in the Leading lamellaMicah Dembo (Boston University)EE/CS 3-180 W5.27-30.08
3:45p-4:15pCoffeeEE/CS 3-176 W5.27-30.08
4:15p-4:45pSecond ChancesEE/CS 3-180 W5.27-30.08
7:00p-8:00pInformal sessions (for people who have energy and will to present and discuss some narrower topics. That would be self-organized, like 2nd chances). EE/CS 3-180 W5.27-30.08

Thursday, May 29

8:30a-9:00aCoffeeEE/CS 3-176 W5.27-30.08
9:00a-9:50aSignal propagation during chemotaxisErin Rericha (University of Maryland)EE/CS 3-180 W5.27-30.08
9:55a-10:45aModeling chemotactic gradient sensing, polarization and motility in Dictyostelium discoideumPablo A. Iglesias (Johns Hopkins University)EE/CS 3-180 W5.27-30.08
10:45a-11:15aCoffeeEE/CS 3-176 W5.27-30.08
11:15a-12:05pNovel signal pathways in tumor cell chemotaxisJohn S. Condeelis (Albert Einstein College of Medicine)EE/CS 3-180 W5.27-30.08
12:05p-2:00pLunch W5.27-30.08
2:00p-2:50pChemotactic cell movement during Dictyostelium development and chick gastrulation Cornelius Weijer (University of Dundee)EE/CS 3-180 W5.27-30.08
2:55p-3:45pBiochemical regulation of cell polarization and actin-based cell motilityLeah Edelstein-Keshet (University of British Columbia)EE/CS 3-180 W5.27-30.08
3:45p-4:15pCoffeeEE/CS 3-176 W5.27-30.08
4:15p-4:45pSecond ChancesEE/CS 3-180 W5.27-30.08
6:30p-8:30pWorkshop dinner at Pagoda in DinkytownPagoda
1417 4th St. SE Minneapolis, MN

Friday, May 30

8:30a-9:00aCoffeeEE/CS 3-176 W5.27-30.08
9:00a-9:50aBacterial chemotaxis: Sophisticated behavior from simple circuitryJohn Sandy Parkinson (University of Utah)EE/CS 3-180 W5.27-30.08
9:55a-10:45aThe chemotaxis receptor cluster revisitedDennis Bray (University of Cambridge)EE/CS 3-180 W5.27-30.08
10:45a-11:15aCoffeeEE/CS 3-176 W5.27-30.08
11:15a-12:05pInferring cellular response to a small stimulus from noise measurements in non-stimulated cellsPhilippe Cluzel (University of Chicago)EE/CS 3-180 W5.27-30.08
12:05p-2:00pLunch W5.27-30.08
2:00p-2:50pFrom molecule to behavior: E. coli’s memory, computation and taxisYuhai Tu (IBM)EE/CS 3-180 W5.27-30.08
2:55p-3:25pSecond Chances + Closing DiscussionEE/CS 3-180 W5.27-30.08
Jonathan B. Alberts (University of Washington) A robustly wrong Listeria motility model, and its redemption
Abstract: Our experimental study of the effect of ActA distribution on the motility of L. monocytogenes indicates that speed is positively correlated with both ActA intensity (amount) and polarity. The agent-based model we used to explore this behavior (from Alberts and Odell 2004) robustly demonstrates the opposite (i.e wrong) polarity relationship with speed. We initially judged this failure as an indication that model parameters, such as the those governing the ActA-actin filament bonds, were "out of tune". Extensive (though not exhaustive) searches in parameter space failed to yield solutions in agreement with experiment. We were ultimately led to the conclusion that our model was topologically incorrect --a mechanistic behavior was improperly represented, or missing altogether. The model is redeemed by inclusion of a cooperative (rather than linearly superposed) restraining force, specifically the explicit frictional drag of filaments on the bacterial surface. The redeemed model robustly captures target experimental behaviors. In light of this experience we reflect on the likely nature of complex dynamical systems in biology and our attempts to represent them in silico. Additionally, we present a one-dimensional partial-differential model (state variables: barbed-ends, actin density, speed of motion) that is instructive as a mathematical synopsis of the agent-based simulation, but fails to demonstrate sensitivity to the details that make all the difference in the complex model (and presumably in the biology).
Claudio Altafini (International School for Advanced Studies (SISSA/ISAS)) Modeling the genome-wide transient response to stimuli in yeast: adaptation through integral feedback
Abstract: At the level of gene expression, the response of yeast to various types of stresses/perturbations is characterized by a short-term transient followed by a return to the basal level (adaptation). A thorough investigation of the transient response to several different stimuli shows a common modulation, functionally and dynamically similar. The adaptation that follows the transient excursion is modeled by means of an integral feedback, with the gene product representing the variable that is fed back. The resulting linear system with input explains sufficiently well the different time constants observable in the transient response while being in agreement with the known experimental degradation rates measurements.
David F. Anderson (University of Wisconsin) Product form stationary distributions for deficiency zero chemical reaction networks
Abstract: The dynamics of chemical reaction networks can be modeled either deterministically or stochastically. The deficiency zero theorem for deterministically modeled systems gives conditions under which a unique equilibrium value with strictly positive components exists within each stoichiometric compatibility class (linear subset of Euclidean space in which trajectories are bounded). The conditions of the theorem actually imply the stronger result that there exist concentrations for which the network is "complex balanced." That observation in turn implies that the standard stochastic model for the reaction network has a product form stationary distribution.
Paul Atzberger (University of California) A stochastic immersed boundary method incorporating thermal fluctuations: Coarse-grained micromechanics
Abstract: The immersed boundary method is a modeling approach traditionally applied to macroscopic systems involving flexible elastic structures which interact with a fluid flow. To use such methods for microscopic systems requires at sufficiently small length scales that thermal fluctuations be taken into account. In this poster we discuss an extension of the immersed boundary method to incorporate thermal fluctuations of both the mechanical structures and the surrounding fluid. The formalism gives a set of stiff SPDE's for which standard numerical approaches perform poorly. We present alternative stochastic numerical methods to integrate the systems of equations. We then discuss how the methods can be used in practice and present results for simulations of a coarse grained model of a lipid bilayer membrane and a molecular motor protein.
Dennis Bray (University of Cambridge) The chemotaxis receptor cluster revisited
Abstract: The cluster of receptors and associated proteins at the 'front end' of the E. coli chemotaxis pathway is a paradigm for membrane complexes in cells. Like focal adhesions and synapses, it acts as a solid-state computational device that amplifies, integrates, and parses chemical signals from the environment and relays the output to the rest of the cell. Ten years ago we proposed a structure for this receptor cluster and suggested how it might provide a basis for the very high sensitivity of cells to certain attractants. In this talk I will revisit the lattice architecture in the light of recent findings and present a radically different mechanism for its amplification. The new model is more firmly based on known molecular events and gives a better understanding of how the cell responds to mixed signals.
Mónica F. Bugallo (SUNY), Petar M. Djuric (SUNY) Solutions to inverse problems of biochemical networks using stochastic methods
Abstract: Advances in the development of models that can satisfactorily describe biochemical networks are extremely valuable for understanding life processes. In order to get full description of such networks, one has to solve the inverse problem, that is, estimate unknowns (rates and populations of various species) or choose models from a set of hypothesized models using experimental data. In this work we discuss signal processing techniques for resolving the inverse problem of biochemical networks using a stochastic approach based on Bayesian theory. The proposed methods are tested in simple scenarios and the results are promising and suggest application of these methods to more complex networks.
Anders E. Carlsson (Washington University) Effects of nonequilibrium processes on actin dynamics and force generation
Abstract: The talk will address two aspects of the connection between nonequilibrium molecular-level processes and properties of actin related to cell motility. 1) The effects of ATP hydrolysis on force generation and polymerization dynamics. Using an extended Brownian-ratchet methodology, it is shown that hydrolysis of bound nucleotide can reduce the stall force of ensembles of actin filaments by a factor of three or more relative to the thermodynamic stall force. The force reduction occurs because the interaction with the obstacle induces hydrolysis at the tip, which converts filament tips temporarily to a depolymerizing state. It is also shown that hydrolysis can lead to overshoots in actin polymerization traces. The overshoots occur when the characteristic time of polymerization is shorter than the nucleotide exchange time on monomers. This effect may be present in cells with sufficiently high concentrations of free barbed ends. 2) The effects of network structure on the contractile stress generated by active myosin II interacting with actin filaments. Using elasticity theory combined with an effective-medium theory, it is shown that the stress generated per myosin is proportional to the average filament length. This leads to estimates of the cytokinesis tension that are much lower than existing estimates. unless the filaments are bundled into inextensible units longer than a filament. Continued contraction requires treadmilling of actin filaments, and the rate of contraction is limited by the filament treadmilling rate.
Yung-Sze Choi (University of Connecticut) Classification of solution to a nonlinear biharmonic equation with negative exponent
Abstract: We study global positive smooth solutions of the geometrically interesting equation: Δ2u + u−q = 0 with q > 0 in R3. When q = 7, it corresponds to some kind of critical index.

When 0 < q ≥ 1, there is no solution, while when q > 1, there is solution with superlinear growth as |x| → ∞. Restricted to linear growth solution, there is no solution for 1 < q < 7. When q = 7, all solutions are radially symmetric. Up to a translation and a dilation, such solution is unique.

Ioana Cipcigan (University of Maryland Baltimore County), Muruhan Rathinam (University of Maryland Baltimore County) Interlaced Euler scheme for stiff stochastic differential equations
Abstract: In deterministic as well as stochastic models of chemical kinetics, stiff systems, i.e. systems with vastly different time scales where the fast scales are stable, are very common. It is well known that the implicit Euler method is well suited for stiff deterministic equations (modeled by ODEs) while the explicit Euler is not. In particular once the fast transients are over, the implicit Euler allows for the choice of times steps comparable to the slowest time scale of the system. In stochastic systems (modeled by SDEs) the picture is more complex. While the implicit Euler has better stability properties over the explicit Euler, it underestimates the stationary variance. In general one may not expect any method to work successfully by taking time steps of the order of the slowest time scale. We explore the idea of interlacing large implicit Euler steps with a sequence of small explicit Euler steps. In particular we present our study of a linear test system of SDEs and demonstrate that such interlacing could effectively deal with stiffness. We also show uniform convergence of mean and variance.
Duncan J. Clarke (University of Minnesota) The cohesin ring is required for centrosome integrity
Abstract: Cohesin is a protein complex which forms a ring structure involved in tethering newly replicated DNA molecules until chromosome segregation in mitosis. We present the unexpected finding that Cohesin Rings are, in addition, needed for the integrity of the centrosome, an organelle that organizes the nucleation of microtubules to form the mitotic spindle. Time lapse microscopy of centrosomes and spindles in living cells revealed that in cells lacking Cohesin, the centrosomes become split during mitosis forming supernumerary spindle poles. This causes the chromosomes to segregate unevenly, leading to aneuploidy. We conclude that the Cohesin Ring is needed for the integrity of the centrosome during mitosis and therefore for proper chromosome segregation.
Philippe Cluzel (University of Chicago) Inferring cellular response to a small stimulus from noise measurements in non-stimulated cells
Abstract: In recent years, there have been significant efforts to characterize the noise associated with the regulation of intracellular processes. Intrinsic fluctuations are often due to the small number of molecules that govern these processes. However, noise is not always caused by a low number of molecules; the regulatory network itself can cause large fluctuations in the number of signaling molecules. For example, systems that have an ultra-sensitive input-output relationship can be effective sources of noise because they not only amplify the input signal but also the associated noise itself. In this picture, systems that are more sensitive to intrinsic spontaneous noise also would be more sensitive to small external perturbations. In linear theory, it is common to analyze, at the equilibrium, spontaneous fluctuations (i.e. noise) in the system in order to predict the dynamical response to a small external perturbation. Here, we extend this simple mathematical framework to infer the cellular response to a small external stimulus by analyzing the noise of non-stimulated cells. We present a combination of experiments on and models of bacterial chemotaxis in E. coli that demonstrate the existence of such a relationship in living cells.
Gheorghe Craciun (University of Wisconsin) Part I: Local and global stability of biochemical reaction network dynamics
Abstract: Local and global stability of biochemical reaction network Dynamics Gheorghe Craciun Modern biological research provides countless examples of biochemical interaction networks. For example, at the intracellular level, the nodes of these interaction networks could be signaling molecules, genes, and gene products. In order to understand the role played by some of these interactions one often faces great difficulties in trying to interpret the effect of positive and negative feedbacks, nonlinear interactions, and other complex signaling between the nodes of the network. We will analyze the connections between reaction network structure and the capacity for complex dynamic behavior. These connections may play an important role in facilitating the understanding of experimental data.
Lance Davidson (University of Pittsburgh) Dynamic contractile F-actin cortex during cell shape change and morphogenesis
Abstract: Joint work with Hye Young Kim and Robert Weaver (University of Pittsburgh, Department of Bioengineering, Pittsburgh PA 15260). Three distinct tissues from the early frog embryo contain either cells that exhibit either no translational movement, mono-polar directed cell migration, or mediolateral cell intercalation. Interestingly, while each cell type exhibits different patterns of cell protrusions they manifest the same stereotypical periodic pattern of F-actin contractions within the pericellular cortex. Contractions form in less than a minute as cortex covering a few square micrometers appears to contract toward a focal point. As contraction progresses the F-actin network increases in density at which point the network appears to depolymerize back to the initial background state. The time-course of contraction followed by depolymerization takes less than two minutes. In order to understand the formation and disassembly of these F-actin contractions we are combining experiments to disrupt or activate the actomyosin cortex with a simple model that captures the basic dynamics of two-dimensional actomyosin networks in the cell cortex. Our model is based on a mechanical representation of myosin II mini-fibrils distributed within a network of polarized actin filaments and appears to capture the initial phase of contraction but not the later disassembly phase of F-actin contractions seen in vivo. Combined analysis of actin dynamics and modeling efforts are needed to understand the complex connections between the molecular mechanisms controlling subcellular mechanics and how these processes shape cells and tissues during development.
Adriana Dawes (University of Washington) Intracellular polarization of motile cells
Abstract: To move in a persistent, directed manner, motile cells must break symmetry and initiate movement that is maintained even after the stimulus is removed. In this poster, I will present a model of intracellular polarization in crawling cells that couples biochemical dynamics with spatially directed force generation. This biologically based model is able to reproduce a number of experimentally observed features including consistent responses to stimuli of varying strength and spontaneous polarization. I will discuss how polarization in other cell types will inform future directions of this model.
Micah Dembo (Boston University) Analysis of actin FLAP dynamics in the Leading lamella
Abstract: Joint work with Igor R. Kuznetsov and Marc Herant. The transport of labeled G-actin from the mid-lamella region to the leading edge in a highly motile malignant rat fibroblast line has recently been studied using fluorescence localization after photo bleaching or FLAP (see Zicha et al.[Zicha2003]). The transit times recorded in these experiments were so fast, that simple diffusion was deemed an insufficient explanation. Since this conclusion has been controversial we here we re-examine the Zicha-FLAP experiments using a two-phase reactive interpenetrating flow formalism to model the cytoplasm and the transport dynamics of bleached and unbleached actin in a moving cell. This new analysis reveals a mechanism that can realistically explain the timing and the amplitude of all the observed FLAP signals in the Zicha-experiments without invoking special transport modalities. The proposed mechanism requires the existence of a small compartment at the leading edge of the lamella where actin polymerization is very fast and where this production is balanced by equally fast mechanical dilatation of F-actin caused by retrograde flow away from the leading edge. If our dilatation hypothesis is correct, the FLAP technique constitutes a novel and very sensitive probe of actin dynamics in a crucial leading edge environment which is otherwise very difficult to interrogate.
Anilkumar Devarapu (University of Louisville) Stochastic simulations of reaction-diffusion models
Abstract: Reaction-Diffusion models are key components of models in developmental biology. These reaction diffusion processes can be mathematically modelled using either deterministic partial differential equations or stochastic simulation algorithms. Here we discuss the stochastic simulations on both linear and non-linear Reaction-diffusion models
Leah Edelstein-Keshet (University of British Columbia) Biochemical regulation of cell polarization and actin-based cell motility
Abstract: I survey our recent work on assembling the modular function and dynamics of signaling casettes that regulate actin-based motility. Arp2/3-mediated branching of actin filaments is regulated by small GTPases of the Rho family. These are modulated by phosphoinositides. Together, such signalling agents determine "front vs rear" in a stimulated cell, where new actin filament ends are nucleated or uncapped inside the cell, and where protrusion or myosin contractility will occur. I describe how we explored such biochemical dynamics in both 1D and 2D cell motility models, and how we analysed their essential features in reduced mathematical caricatures. This work is joint with AFM Maree, AT Dawes, A Jilkine, Y Mori, and V Grieneisen. It is supported by NSERC, NSF, and MITACS.
Sergei Fedotov (University of Manchester) Anomalous diffusion, tumor growth and random walk models
Abstract: The theory of anomalous diffusion is well-established and leads to the integral equations or the alternative fractional diffusion equations for number densities. Despite the progress in understanding the anomalous transport most work has been concentrated on the passive density of the particles, and comparatively little is known about the interaction of non- standard transport with reactions. This work is intended to address this issue by utilising the random walk techniques in order to model the anomalous diffusion with reactions. Example is the tumor's cells migration and proliferation (Phys. Rev. Lett. 98, 118101 (2007)).
Henrik Flyvbjerg (Technical University of Denmark) Cell motility as persistent random motion: theories from experiments
Abstract: Experimental time series for trajectories of motile cells may contain so much information that a systematic analysis will yield cell-type-specific motility models. We show how here, using human keratinocytes and fibroblasts as examples. The two models that result, seem to reflect the cells' different roles in the organism, and show that a cell has a memory of past velocities. The models distinguish quantitatively between various surfaces' compatibility with the two cell types.
Arnab Ganguly (University of Wisconsin) Simulating discrete biochemical reaction systems
Abstract: The stochastic simulation algorithm, or Gillespie Algorithm, is a tool used to simulate discrete biochemical reaction systems when there are a small to moderate number of molecules. The Gillespie Algorithm has been adapted to handle systems with delays (such as with gene transcription and translation) and approximations (such as tau leaping) have been developed in order to increase computation speed. In this poster we will model discrete biochemical systems via a random time change representation. We will then demonstrate how natural and efficient modifications of the stochastic simulation algorithm arise from such a representation. Also, we will use this representation to show how to incorporate post-leap checks in the tau-leaping algorithm.
Margaret Gardel (University of Chicago) F-actin dynamics regulate force transmission at focal adhesions
Abstract: The ability of cells to spatially and temporally regulate traction forces on their extracellular matrix is fundamental to tissue morphogenesis and directed cell migration. Forces generated in the actin filament (F-actin) cytoskeleton are transmitted through the cell plasma membrane to the extracellular matrix via mechano-sensitive focal adhesions1. In migrating cells, F-actin and focal adhesions exhibit stereotypical patterns of assembly, disassembly and motion2-8. It is well appreciated that an intact F-actin cytoskeleton is required for cellular force generation; however, the role of F-actin motion dynamics in force generation is unknown. We show here that F-actin motion spatially correlates with traction stresses on the extracellular matrix. Near the cell edge, traction stress and F-actin speed are inversely correlated, suggesting that focal adhesions strengthen by slowing F-actin and engaging it to the stationary extracellular matrix. However, instead of observing maximal traction stress when F-actin motion is minimized, we find that an intermediate speed of F-actin motion marks a switch to focal adhesion weakening. The switch from focal adhesion strengthening to weakening is not correlated with focal adhesion protein density, age, stress magnitude, assembly/disassembly status or subcellular position. In contrast, the F-actin speed associated with maximal traction stress and the transition to adhesion weakening is strikingly robust. Thus, we identify F-actin motion dynamics as an important regulator of focal adhesion-mediated traction forces at the leading edge of migrating cells.
Melissa K. Gardner (University of Minnesota) Microtubule assembly dynamics at the nanoscale
Abstract: Joint work with Henry T. Schek2, Alan J. Hunt2, and David J. Odde1. Microtubule ends are intrinsically unstable, and although this property is critical for establishing cellular morphology and motility, the molecular basis of assembly remains unclear. Our 3D mechanochemical model for microtubule dynamic instability predicts that a spatially extended GTP cap allows for highly variable growth dynamics, and specifically that substantial nanoscale shortening of the microtubule tip could occur during a microtubule growth phase. Here we use optical tweezers to track microtubule polymerization against microfabricated barriers, permitting unprecedented spatial resolution. We find that microtubules exhibit extensive nanometer-scale variability in growth rate, and often undergo shortening excursions, in some cases exceeding 5 tubulin layers, during periods of overall net growth. This result indicates that the GTP cap does not exist as a single layer as previously proposed. Rather, simulations that rely on an exponentially distributed GTP-Cap qualitatively reproduce the experimentally observed variability in microtubule growth. 1Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN
2Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI
Peter W. Glynn (Stanford University), Peter J. Haas (IBM Research Division) An introduction to discrete-event simulation
Abstract: Biochemical systems can often be viewed as discrete-event systems, i.e., as systems that make stochastic state transitions at a strictly increasing sequence of random times. We survey a number of topics pertinent to modeling and simulation of such systems. We first describe several basic models for discrete-event systems, such as generalized semi-Markov processes, stochastic Petri nets, and continuous time Markov chains, and discuss the interplay between the choice of modeling formalism, the compactness of the model representation, and the computational complexity of the resulting simulation algorithm. We then outline a collection of techniques for increasing the efficiency of a simulation, as well as for efficiently estimating the sensitivity of a discrete-event system model with respect to one or more model parameters.
Nir Shachna Gov (Weizmann Institute of Science) Coupling the cytoskeleton to the membrane: driving dynamic cellular shape transitions
Abstract: The outer membrane of a living cell is very different from an inert lipid bilayer or a vesicle. Most notably, there exists a strong coupling between the membrane and the underlying cytoskeletal network of the cell. The cytoskeleton is a dynamic formation of proteins that is continuously reshaping itself, and in the process applies forces to the membrane. The membrane of a living cell is therefore constantly deformed by the forces of the underlying cytoskeleton. The energy produced by the cell's metabolism, in the form of ATP, drives the motion of the cytoskeleton and membrane through the polymerization of cytoskeletal filaments (actin and microtubules), the action of cytoskeleton-bound molecular motors and membrane-bound ions pumps. The cytoskeleton modifies the physical properties, such as the tension, fluctuation amplitude and effective bending modulus of the lipid membrane. In turn, the cytoskeletal organization can be influenced by the membrane shape (curvature) and tension. We describe several theoretical models of the physics of an active cytoskeleton and membrane and their coupling with the cell metabolism. The cytoskeleton-membrane coupling can lead to dynamic instabilities which are manifested as shape transitions of the membrane from the uniform flat configuration to one with finger-like protrusions. These transitions are coupled with composition phase separation inside the membrane, and are triggered by the active forces of the cytoskeleton. A similar instability is proposed as a model for the initiation of the contractile ring in dividing cells. Furthermore, traveling (propagating) waves can also arise when there are opposing forces of protrusion and contraction, or due to the effect of calcium ion influx. We compare these results to the observed behavior of living cell membranes, which exhibit a variety of dynamic behaviors.
Dirk Hartmann (Ruprecht-Karls-Universität Heidelberg) Mathematical and computational tools for cell-mechanobiology
Abstract: Mechanical properties are a key feature in a wide rage of animal cell functions, including growth, motility, and gene expression. On the poster, we outline different mathematical and computational tools for theoretical investigations of the mechanobiology of cells. Modelling mechanics of cytoskeletal networks often discrete microscopic models in terms of energy functionals are employed. However macroscopic continuum models are usually preferable form a computational point of view. But finding such macroscopic descriptions is often a non-trivial task. Considering microscopic models given in terms of free energies Gamma-convergence is the ideal framework for rigorously bridging the gap between discrete microscopic and continuous macroscopic models. On this poster mechanics of red blood cells are considered to show how such a multiscale framework can be employed to derive appropriate constitutive laws. The second focus of this poster are computational tools for studying the mechanobiology of cells. We outline two approaches: a Lagrangian approach, which represents evolving domains via transformations of a fixed grid, and an Eulerian approach, which characterises evolving domains implicitly using levelset methods. Both approaches are capable of coupling surface and bulk mechanics, as well as chemical and mechanical processes within one implicit time-stepping scheme.
Peter Hinow (University of Minnesota) A model for transfer phenomena in structured populations
Abstract: P-glycoprotein (P-gp) is known to cause resistance to cancer chemotherapy as it is able to remove toxic substances from the cytoplasm of a cell. Recent experimental work by Levchenko et al. shows that cells rich in P-gp are able to transfer part of their P-gp to other cells and thereby may confer resistance. We propose a mathematical model for the transfer of a scalar quantity in a structured population. It is shown that the solutions of this 'pure transfer' model converge to a Radon measure. We add to this model production of P-gp and random fluctuations in P-gp content. For the amended model we show the existence of a globally asymptotically stable steady state, provided that the rate of P-gp transfer is sufficiently small. This is joint work with Pierre Magal (University of Le Havre, France) and Glenn F. Webb (Vanderbilt University).
Rick Horwitz (University of Virginia) Actin and a-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor independent manner
Abstract: Joint work with Colin K. Choi 1,2, Miguel Vicente-Manzanares2, Jessica Zareno2, Leanna A. Whitmore2, and Alex Mogilner3. We have developed a new model for the assembly and maturation of nascent adhesions. Using dual label imaging and high resolution TIRF microscopy, we show that nascent adhesions assemble and are stable only within the lamellipodium. The assembly is myosin II-independent and requires actin polymerization. A computational model has been developed that accommodates the quantitative data on the dynamics of the nascent adhesions and the linkage of their assembly to actin polymerization. As the back of the lamellipodium moves past the nascent adhesions, they either disassemble as the protrusion continues to advance or begin to grow and elongate and mature as the protrusion pauses. Rescue of a myosin IIA knockdown with a motor-inhibited mutant of myosin IIA shows that the cross-linking function of myosin II is sufficient to promote adhesion maturation. Using an RNAi knockdown of ?-actinin, we demonstrate that a-actinin-actin filaments serve as a template that guides the centripetal elongation of the nascent adhesion. Measurements of paxillin dynamics and clustering using correlation microscopy show that adhesions tend to assemble by addition of monomers or small aggregates while they disassemble as large aggregates. From these studies, a new model emerges for adhesion assembly and maturation that clarifies the relative contributions of actin polymerization, stabilization and myosin II motor activity to adhesion dynamics. 1 Department of Biomedical Engineering and 2 Cell Biology, University of Virginia, Charlottesville, Virginia 22908; 3Department of Neurobiology, Physiology and Behavior and Department of Mathematics, University of California, Davis, California 95618.
Pablo A. Iglesias (Johns Hopkins University) Modeling chemotactic gradient sensing, polarization and motility in Dictyostelium discoideum
Abstract: In this talk I will discuss our group's efforts at elucidating the mechanisms underlying chemotaxis. Using known biochemical data, we have developed mathematical models that can account for many of the observed chemotactic behavior of the model organism Dictyostelium. I will discuss experiments used to test these models. Finally, I will describe how information-theoretic methods can be used to evaluate the optimality of the gradient sensing mechanisms.
Ken Jacobson (University of North Carolina) New methods to study motile phenomena
Abstract: We are currently attempting to understand how the basic processes of contractility, protrusion and adhesion are integrated to produce cell migration. This is an intellectually challenging problem that requires new approaches. The overall plan is to test an in silico model developed by A. Mogilner and colleagues for migration and check this model by perturbing these basic processes locally using photomanipulative techniques to see if the experimentally determined changes in migration can be accounted for by the model. The feasibility of two types of perturbations has now been demonstrated. Caged actin binding proteins and peptides derived from Focal Adhesion Kinase (FAK) can be uncaged and produce dramatic phenotypes. A complementary loss of function technique, EGFP-chromophore-assisted laser inactivation (EGFP-CALI), has been applied locally to several actin binding proteins including EGFP-a-actinin, EGFP-Mena and EGFP-capping protein, again with strong phenotypes. Photochemical mechanisms mediating CALI will be discussed.

I will also describe a graph theoretic approach to modeling motile phenomena that has been developed in collaboration with Gabriel Weinreb, Maryna Kapustina and Tim Elston. The causal map (CMAP) is a course-grained biological network tool that permits description of causal interactions between the elements of the network which leads to overall system dynamics. On one hand, the CM CMAP is an intermediate between experiments and physical modeling, describing major requisite elements, their interactions and paths of causality propagation. On the other hand, the CMAP is an in independent tool to explore the hierarchical organization of cell and the role of uncertainties in the system. It appears to be a promising easy-to-use technique for cell biologists to systematically probe v verbally formulated, qualitative hypotheses. We apply the CMAP to study the phenomenon of contractility oscillations in spreading cells in which microtubules have been depolymerized. Supported by the NIH Cell Migration Consortium, IK54GM64346.

Hye-Won Kang (University of Wisconsin) Multiscale methods in a heat shock response model
Abstract: We analyze a heat shock response model developed by Srivastava, Peterson, and Bently (2001) to find appropriate scaling for the abundance of molecules of chemical species and for chemical reaction rates. Extending the method introduced in the paper by Ball, Kurtz, Popovic, and Rempala (2006), we apply the multiple scaling method to the various range of the abundance of chemical species and the chemical reaction rate constants. In this method, the complicated original system is split into several subsystems with separate fast, intermediate, and slow processes by using the approximated scaled processes with appropriate time change. Then, we can approximate the state of the system from the state of the reduced subsystems. In the slow time scale, we identify behavior of fast processes since they already start to move while the slow species remain mostly constant. In the fast time scale, we identify behavior of the slow processes driven by averaged behavior of fast processes. Our goal is to find an appropriate scaling that makes the abundance of molecules of each chemical species well-balanced. To make each chemical species balanced, the maximal order of magnitude of the reaction rates of production for each chemical species must be the same as the maximal order of magnitude of the reaction rates of consumption. We also need a balance condition between the maximal order of magnitude of collective reaction rates of inflow and outflow in each atom graph. In case any of balance conditions are not satisfied, we put restriction on the range of time change exponent. In this poster, I will introduce multiscale method briefly and give a simulation result for one set of exponents meeting our balance conditions.
Yiannis N. Kaznessis (University of Minnesota) Multiscale models for synthetic biology
Abstract: The nascent field of synthetic biology offers the promise of engineered gene networks with novel biological phenotypes. Numerous synthetic gene circuits have been created in the past decade, including bistable switches, oscillators, and logic gates. Despite a booming field and although recently developed designs of regulatable gene networks are ingenious, there are limitations in routinely engineering synthetic biological systems. Indeed, there is a need for rationalizing the design of novel regulatable gene networks that can be used in useful applications. We are developing multiscale mathematical tools to assist synthetic biology efforts. Why are multiscale models necessary to assist synthetic biology, and not simply apply the mathematics developed to model kinetic and thermodynamic processes in living organisms? Because, although the principles of thermodynamics, kinetics and transport phenomena apply to biological systems, these systems differ from industrial-scale chemical systems in an important, fundamental way: they are occasionally far from the thermodynamic limit. Indeed, using ordinary differential equations for simulating the reaction kinetics of these systems can be distinctly false. The need arises then for stochastic models that account for inherent, thermal noise, which is manifest as phenotypic distributions at the population growth/interaction levels. In the presentation, we will discuss synthetic biological systems, the development of multiscale models to capture the phenotypic behavior of these systems and we will present examples of model-driven synthetic bioengineering.
Yiannis N. Kaznessis (University of Minnesota) Stochastic models for intracellular reaction networks
Abstract: In the presented work we will describe how to rationalize synthetic biology using model-driven, molecular-level engineering principles. In the poster we will focus on the theoretical effort to develop an algorithm for simulating biomolecular systems across all relevant time and length scales; from stochastic-discrete to stochastic-continuous and deterministic-continuous models, we are developing the theoretical foundation for accurately simulating all biomolecular interactions in transcription, translation, regulation and induction and how these result in phenotypic probability distributions at the population level.
Kyung Hyuk Kim (University of Washington) Stochastic control analysis for biological reaction systems
Abstract: We have investigated how noise propagation in biological reaction networks affects system sensitivities. We have shown that the sensitivities can be enhanced in one region of system parameter values by reducing sensitivities in another region. We have applied this sensitivity compensation effect to enhance the amplification of a concentration detector designed by using an incoherent feed-forward reaction network. We have also shown that metabolic control analysis can be extended for stochastic reaction systems by providing new versions of the summation and connectivity theorems.
Samuel Kou (Harvard University) Subdiffusion and reaction networks in biophysics
Abstract: In recent years, single-molecule experiments have emerged as a powerful means to study biophysical/biochemical processes; many new insights are obtained from this single-molecule perspective. One phenomenon recently observed in single-molecule biophysics experiments is subdiffusion, which largely departs from the classical Brownian diffusion theory. In this talk, by introducing fractional Gaussian noise into the generalized Langevin equation, we propose a model to describe the subdiffusion. We will study the analytical properties of the model, compare the model predictions with experiments, look at its connection with reaction networks, and explore the implications of the model on enzyme reactions.
Michael M. Kozlov (Tel Aviv University) Actin organization at the cell edge: mechanism for formation of lamellipodium -lamellum interface
Abstract: The complex system of actin filaments spanning the volume of a moving cell can be subdivided into distinct zones differing in their dynamic behaviour, structure and function and ordered in space sequentially beginning from the cell leading edge towards the cell interior. The first two zones are the lamellipodium, which underlies the cell membrane at the leading edge, and the lamellum adjacent to the lamellipodium and propagating further into the cell volume. The lamellipodium and lamellar actin networks do not overlap; they are separated by a distinct interface marked by an abrupt change of the velocity of the retrograde actin flow, and by a sharp change of the actin network density and structure. Revealing the physical forces responsible for the generation and dynamics of the lamellipodium-lamellum interface is of a primary importance for understanding the factors which govern organization of actin at the cell front into the spatially segregated and essentially distinct sub-systems. The goal of the present work is to propose a physical mechanism for this phenomenon. Based on the existing knowledge on the mechanical properties of actin gels, we consider the lamellipodium actin network as a two-dimensional elastic medium, which slides towards the cell centre over a row of focal adhesions and exerts a friction-like interaction with the latter. We show that the friction-like interaction between the actin gel and the focal adhesions results in formation of a lamellipodium boundary passing through the row of the FAs and having a shape similar to that observed within cells. This boundary is suggested to represent the lamellipodium-lamellum interface. We further consider advancing of the lamellipodium-lamellum interface to a new row of focal adhesions.
Peter R. Kramer (Rensselaer Polytechnic Institute) Prescribing thermal forcing for physical systems
Abstract: I will describe the principles, particularly the fluctuation-dissipation theorem, involved in adding the appropriate stochastic driving terms to represent the effects of finite temperature on a given physical system. The concepts will be described both for an elementary example as well as for the more complicated immersed boundary method simulation scheme for flexible structures coupled to an ambient fluid.
Peter R. Kramer (Rensselaer Polytechnic Institute) Theoretical framework for microscopic osmotic phenomena
Abstract: My main intention in this seminar is to think through, in simple physical terms, how osmotic pressure (for a semipermeable membrane confining a solute) manifests itself microscopically. That is, I will approach the question simply in terms of mechanical forces between the solute and membrane, and the pressure in the fluid. Somehow I am a little concerned that I may be naive about some aspects, and I would appreciate the current IMA visitors pointing out to me where my reasoning may be inadequate! The reason for this investigation was the recognition that the classical statistical mechanical formula for osmotic pressure (van't Hoff's law) requires corrections when some of the idealized assumptions (infinitesmal particles, hard-wall membrane) break down. In the physical modeling and numerical simulation of sub-micron scale systems, these deviations from the idealized limits appear to be relevant. I'll explain the change to the classical formulas in terms of simple examples; in particular the osmotic pressure registered in the fluid must be distinguished from that exerted on the membrane. This discussion will primarily involve elementary statistical mechanics and fluid mechanics. Probability arises only in the prescription of the random configurations of the solute particles subject to the confining potential of the membrane.
Thomas G. Kurtz (University of Wisconsin) Analyzing stochastic models
Abstract: Classical stochastic models for chemical reaction networks are given by continuous time Markov chains. Methods for characterizing these models will be reviewed focusing primarily on obtaining the models as solutions of stochastic equations. The relationship between these equations and standard simulation methods will be described. The primary focus of the talk will be on employing stochastic analytic methods for these equations to understand the multiscale nature of complex networks and to exploit the multiscale properties to simplify the network models.
Pilhwa Lee (University of Colorado) Simulation of concentration-dependent contraction of cell
Abstract: A mathematical modeling and simulation for concentration-dependent contraction of cell is shown in an illustrative way. The cell is supposed to have actomyosin fibers parallelly in cytoplasm. Those fibers are sensitive to local calcium concentration regarding elastic stiffness and resting length by Hill-type curves. Initially the calcium is low in intracellular domain, and high in extracellular domain. With the membrane permeable to calcium, actomyosin network gets activated and contracted by increased calcium inside. By the water semi-permeability of the membrane and the osmotic effect, the volume change is available in the course of contraction. Membrane and fibers being moving in a viscous fluid, the spatio-temporal dynamics of ion concentration are possible by the computational framework of the immersed boundary method with advection-electrodiffusion.
James C. Liao (University of California) Closing plenary talk: Metabolic engineering and metabolic modeling: where do we go from here?
Abstract: Engineering intracellular metabolism has a long history, dated back to the late 1950s. The field has enjoyed significant attention in recent years, particularly because of the energy and environmental concerns. Many success stories have highlighted the feasibility of engineering intracellular metabolism to achieve a designed function. In almost all cases, the bottleneck of the problem resides on the biological side. With some exceptions, mathematical modeling has rarely played a predictive role in this development, mainly because of the lack of appropriate model structure and useful parameters. This talk will discuss a few examples of metabolic engineering and examine the role of mathematical modeling in these developments. In particular, we will present an en ensemble modeling technique that aims to narrow the gap been experiment and model prediction.
Karen Lipkow (University of Cambridge), David Odde (University of Minnesota) Model for protein concentration gradients in the cytoplasm
Abstract: Intracellular protein concentration gradients are generally thought to be unsustainable at steady-state due to diffusion. Here we show how protein concentration gradients can theoretically be sustained indefinitely through a relatively simple mechanism that couples diffusion to a spatially segregated kinase–phosphatase system. Although it is appreciated that such systems can theoretically give rise to phosphostate gradients, it has been assumed that they do not give rise to gradients in the total protein concentration. Here we show that this assumption does not hold if the two forms of protein have different diffusion coefficients. If, for example, the phosphorylated state binds selectively to a second larger protein or protein complex, then a steady-state gradient in total protein concentration will be created. We illustrate the principle with an analytical solution to the diffusion-reaction problem and by stochastic individual-based simulations using the Smoldyn program. Looking at the example of bacterial chemotaxis, our model accounts for gradients of total CheY and CheZ, which were observed, but not explained, previously. We argue that protein gradients created in this way need to be considered in experiments using fluorescent probes and could in principle encode spatial information in the cytoplasm.
Karen Lipkow (University of Cambridge) Smoldyn, a novel simulator for cellular systems biology
Abstract: Joint work with Steven S. Andrews (The Molecular Sciences Institute, Berkeley, MA).

Smoldyn is a computer program for performing detailed simulations of cell biology. Proteins and other molecules of interest are represented by individual point-like particles that diffuse within a continuous (non-lattice) space. Smoldyn accurately and efficiently simulates diffusion, first and second order chemical reactions, allostery, and a wide variety of molecule-membrane interactions. As in the eponymous Smoluchowski theory, simulated bimolecular reactions occur when reactants diffuse closer together than a so-called binding radius. Smoldyn was written on OS X in C and OpenGL. It is open source, multi-platform, and easy to use, running on any machine from laptop to computer cluster. Smoldyn is freely available, designed for both the research and teaching communities. We present the algorithm and its speed performance, and its application in modelling various aspects of the bacterial chemotaxis system.

Wolfgang Losert (University of Maryland) Quantitative analysis of stream formation during dictyostelium chemotaxis
Abstract: Joint work with C.P. McCann1,2, P.W. Kriebel1, E.C. Rericha2, C.A. Parent1. Upon nutrient deprivation, the social amoeba Dictyostelium discoideum enter a developmental program allowing them to aggregate and differentiate into a multicellular organism made of spores atop a stalk of vacuolated cells. During the aggregation process individual cells sense and migrate up a chemoattractant gradient of cyclic adenosine monophosphate (cAMP), relaying the signal by synthesizing and releasing additional cAMP. This process leads to a characteristic chain migration where cells align in a head-to-tail fashion and migrate in streams. We have quantitatively analyzed time-lapse images of cells as they migrate in streams. We find that the average cell migration speed and the formation of streams are sensitive to cell plating density. At a density of 7x104 cells/cm2 cells stream with an average speed of ~10 micron/min outside steams, while at 2x104 cells/cm2 cells do not stream and move with an average speed of ~5 micron/min. In addition, for a given plating density, the volume of fluid above the cells has a strong influence on the formation of streams, suggesting that excess extracelluar fluid effectively dilutes cell-to-cell signals. We are currently performing cell mixing experiments with fluorescently labeled cells to assess the speed of cells both inside and outside streams. Our findings provide insights into the requirements for signal relay during chemotaxis and highlight the importance of environmental conditions for cell migration. 1Laboratory of Molecular and Cellular Biology, CCR, NCI, NIH, Bethesda, MD;
2Dept. of Physics, University of Maryland, College Park, MD
Denise Montell (Johns Hopkins University) Developmental regulation of cell motility
Abstract: In normal development and tumor metastasis, epithelial cells can acquire migratory and invasive properties. Border cells in the Drosophila ovary provide a genetic model for such behaviors. Earlier work has shown that JAK/STAT signaling is critical to specify the migratory population and sustain their motility. In a genetic screen for new mutations that affect border cell motility, we identified the gene apontic. Apontic, a nuclear protein, converts an initially graded pattern of STAT activity into an all-or-nothing response. This defines and limits the invasive border cell population. Apt functions as a feedback inhibitor of STAT, providing a molecular mechanism to explain a classic problem in embryology: how a graded signal can generate discrete cellular responses. This work, which includes a mathematical model, elucidates one mechanism to limit cell invasion in vivo.
Hans G. Othmer (University of Minnesota) Stochastic aspects of actin filament dynamics
Abstract: Actin polymerization and network formation are key processes in cell motility. Numerous actin binding proteins that control the dynamic properties of actin networks have been studied and models such as the dendritic nucleation scheme have been proposed for the functional integration of at least a minimal set of such regulatory proteins. In this talk we will describe recent work on the evolution of the distribution of filament lengths and nucleotide profiles of actin filaments from both the deterministic and stochastic viewpoints. For the latter we develop a master equation for the biochemical processes involved at the individual filament level and simulate the dynamics by generating numerical realizations using a Monte Carlo scheme. A new computational algorithm that is far more efficient than standard methods will also be described.
John Sandy Parkinson (University of Utah) Bacterial chemotaxis: Sophisticated behavior from simple circuitry
Abstract: Motile bacteria seek optimal living habitats by following gradients of attractant and repellent chemicals in their environment. The signaling machinery for these chemotactic behaviors, although assembled from just a few protein components, has extraordinary information-processing capabilities. Escherichia coli, the best-studied model, employs a networked cluster of transmembrane receptors to detect minute chemical stimuli, to integrate multiple and conþicting inputs, and to generate an ampliÞed output signal that controls the cell's þagellar motors. Signal gain arises through cooperative action of chemoreceptors of different types. The signaling teams within a receptor cluster may be built from trimers of receptor dimers that communicate through shared connections to their partner signaling proteins.
Johan Paulsson (Harvard Medical School) Fundamental limits on the suppression of randomness in biology
Abstract: Living cells contain such low numbers of active genes, RNAs and proteins that random fluctuations in concentrations arise spontaneously. Because many biological processes require reliability and precision, cells are thought to deal with this problem by using negative feedback control loops, correcting perturbations by increasing synthesis at high concentrations and decreasing it at low concentrations. Negative feedback has been systematically studied in control theory, but focus has been on macroscopically large systems subject to external perturbations - like airplanes in random gusts of wind - while other principles arise in discrete molecular-scale probabilistic processes. Many biological control loops are also strongly nonlinear, and crucial aspects are often unknown. Such systems are typically considered impossible to analyze: how can we make quantitative statements about strongly nonlinear stochastic systems if we do not even know the nature of the nonlinearities? By combining exact analytical tools from functional analysis, information theory and statistical physics, I will show that seemingly mild constraints, such as short delays or finite numbers of control molecules, can place fundamental limits on noise suppression that no arbitrarily elaborate feedback system could ever overcome - hard physical bounds that can be derived explicitly. Using approximate methods for families of feedback systems, I will also show how the limits arise because different types of noise are suppressed according to incompatible principles, generating frustration trade-offs where reducing one type of variation inevitably amplifies another. Finally I discuss partial loopholes in the general laws where counterintuitive mechanisms can circumvent the trade-offs to some extent. The general results are illustrated by bacterial plasmids, where large fluctuations promote extinction and where numerous mechanisms have evolved to approach the physical limits. I will emphasize intuitive reasoning and physical observables throughout, and show some preliminary experiments.
Alka A. Potdar (Vanderbilt University) Cellular dynamics simulations of MCF-10A cell random migration in 2-D
Abstract: Coauthors: Junhwan Jeon [1], Alissa M. Weaver [2] and Peter T. Cummings [1,3]. We have implemented the cellular dynamics simulation methodology (originally developed for bacterial migration) to describe the random migration of MCF-10A pbabe, neuN and neuT cells using the experimental parameters extracted for each cell type, by the application of bimodal analysis technique developed by us. The Bimodal framework inspired from the bacterial run-tumble scheme segregates mammalian cell tracks into alternating directional and re-orientation modes. We find from simulations that the HER-2 transformed neuT cells have higher random motility coefficient compared to the control pbabes. [1]Department of Chemical Engineering, Vanderbilt University, Nashville TN
[2]Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, TN
[3]Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN
Michael C. Reed (Duke University) Opening plenary talk: Stochastic analysis is the fundamental tool for understanding biological function
Abstract: Several deterministic models will be presented to illustrate the special types of mechanisms that regulate and control cell metabolism. Stochastic analysis can be used to investigate such highly nonlinear deterministic dynamical systems that typically operate far from equilibrium. Examples will be given that show how specific biological system properties depend on the natural stochasticity inherent in diffusion processes and in the making and breaking of chemical bonds. On many different space and time scales, evolution has selected stochastic mechanisms for accomplishing specific biological functions. Finding, characterizing, and explaining these mechanisms requires cooperative research by biologists and stochastic analysts. The tasks are daunting because biology is really hard.
Grzegorz A. Rempala (University of Louisville) Inferring an underlying reaction network from the data
Abstract: Consider the system of reaction rate equations (RRE) describing a chemical network with the reaction rate constants considered to be unknown parameters. The talk shall describe a statistical approach to identifying the "most likely network" from a given set of RRE coefficient estimates. The idea relies on mapping the estimated reaction constants into an appropriate convex region of a network stochiometric space in order to identify the reactions which are most likely to span that region. This approach reduces the original problem to inferring parameters of a certain multinomial distribution which may be solved using the general methods of algebraic statistics.
Erin Rericha (University of Maryland) Signal propagation during chemotaxis
Abstract: The social amoebae Dictyostelium and human leukocytes possess the ability to polarize and move in a directed fashion in response to chemical signals. We are interested in understanding how cells transduce shallow external chemotactic signals into highly polarized cellular responses, which are required for directed cell migration. By tagging various signaling proteins with the green fluorescent protein (GFP) we have been able to visualize in live cells where and when various cascades are activated. This has led us to propose a novel mechanism that explains how chemotactic gradients are amplified by signal relay. Our research projects are designed to provide insight on the role of various signaling cascades in chemotaxis and have direct bearing on the understanding of clinically important processes as such leukocyte migration to sites of inflammation as well as cancer metastasis.
Howard Salis (University of California) Predicting translation rate from sequence
Abstract: The reliable genetic engineering of bacterial systems would be greatly aided by a more quantitative and predictive understanding of gene expression. In many synthetic biology applications, the production rate of a protein needs to be precisely tuned to optimize some performance characteristic of the genetic system. A typical application might require selecting the optimal expression level of enzymes in a metabolic pathway. The production rate of a protein can be precisely tuned by varying the mRNA sequence of the 5' UTR (untranslated region), including the ribosome binding site (RBS), that precedes the protein's coding sequence. However, there is currently no quantitative model that can predict an RNA sequence that yields a desired production rate of protein. We have developed and experimentally validated a statistical thermodynamic model of translation initiation in Escherichia coli. The model quantifies the effects of the important RNA, RNA-RNA, and RNA-protein interactions and determines the resulting translation initiation rate of a specified mRNA transcript. We combine the quantitative model with Monte Carlo sampling to create a design method that generates synthetic 5' UTRs. The user inputs a protein coding sequence and a desired translation initiation rate and the design method will generate the corresponding RNA sequence. We measure the accuracy of the design method by generating numerous synthetic 5' UTRs that drive the expression of the fluorescent protein RFP in a simplified test system. We then compare the design method's predictions with flow cytometry data from a test system. The design method is capable of accurately generating RNA sequences that yield the desired translation rate, with rates varying across three orders of magnitude. The presented model and method is a key foundational technology that will enable us to more rationally engineer synthetic biological systems. With the emergence of lower cost large-scale DNA synthesis and the rapid assembly of genetic systems, the development bottleneck now shifts towards identifying the DNA sequence that ultimately yields a desired system behavior. These and other quantitative and predictive models aim to provide that much-needed missing link.
Sebastian Ambrose Sandersius (Arizona State University) Modeling cell rheology: microrheology of viscoelastic networks
Abstract: Recently, a computational model addressing cell biomechanics has been introduced, called the Subcellular Element Model (SEM). The model is primarily designed to represent deformable cells in multi-cellular systems, but can also be used to represent a single cell in more detail. Within the model framework, a cell is represented by a collection of elastically coupled elements, interacting with one another via short-range potentials, and dynamically updated using over-damped Langevin dynamics. We have tested whether the model yields viscoelastic properties consistent with those measured on single living cells and reconstituted cytoskeletal networks. Employing methods of microrheology we find that weak power law rheology emerges. With further phenomenology of treating the cytoskeleton as a viscoelastic network, we show here a novel one-dimensional model, which as well displays intermediate time regime/weak power law rheology.
Christian Schmeiser (Universität Wien) A continuum model of the cytoskeleton dynamics in lamellipodia
Abstract: The lamellipodium is the movement organ of several types of crawling cells. Motility is driven by the dynamics of the actin cytoskeleton, a flat network of polymers. The dynamics is influenced by actin (de)polymerization, by crosslinking of polymers, by their stiffness, by adhesion of the network to the substrate through transmembrane proteins, by active contraction of the network by motor proteins, and by the mechanical properties of the cell membrane. In a recent modelling effort, these effects are modelled on a microscopic scale, where the elastic response of individual filaments and the stochastic properties of protein reactions are taken into account. Then, by a homogenization procedure, continuum models for the cytoplasm in a lamellipodium are derived. The derivation of this new class of models, their mathematical properties, as well as results of numerical simulations will be presented.
Rishi Srivastava (University of Wisconsin) Stochastic modeling of vesicular stomatitis virus(VSV) growth in cells: An application of order statistics to predict replication delays
Abstract: Although viruses are the smallest organisms with the shortest genomes, they have major impacts on human health, causing deadly diseases (e.g., influenza, AIDS, cancer) on a global scale. To reproduce, a virus particle must infect a living cell and divert biosynthetic resources toward production of virus components. A better mechanistic understanding the infection cycle could lead to insights for more effective anti-viral strategies. However, simulating the virus infection cycle is a computationally hard problem because some species fluctuate rapidly while others change gradually in number. We study vesicular stomatitis virus, an experimentally accessible virus for which we have developed a deterministic kinetic model of growth (Lim et al, PLoS Comp Bio, 2006). Stochastic simulation of VSV genome encapsidation is a computationally-intensive chain reaction that produces rapid fluctuations in the nucleocapsid(N) protein that associates with the genome. Analytical results from order statistics enable us to avoid explicit tracking of all intermediate species, with significant reduction in computational burden. This approach can be generalized to a broad class of stochastic polymerization reactions where multi-step chain reactions are modeled as a single reaction with time-delay.
Benjamin L. Stottrup (Augsburg College) Tenascin-C is upregulated at the end of the cell cycle in proliferating NIH 3T3 fibroblasts
Abstract: Joint work with Michael Halter1, Kurt J. Langenbach2, Alex Tona3, Anne L. Plant1, John T. Elliott1 Tenascin-C expression is frequently upregulated during wound healing, inflammation, and tumorigenesis. Using live cell automated microscopy, we quantified the fluorescence intensity from individual NIH-3T3 fibroblasts stably transfected with a tenascin-C promoter driving a destabilized eGFP reporter. Hundreds of individual cells were followed throughout the cell cycle during live cell imaging experiments lasting 62 hours. We will describe techniques used to track these cells as they migrate. We observed that the GFP production in individual cells increased as they approached mitosis. On average the increase began when cells were approximately 60% through the cell cycle, suggesting that the tenascin-C promoter is more active at the end of the cell cycle. We conclude that the increase in GFP within individual cells was unlikely due to a systematic change in the degradation of GFP because we found no correlation between the GFP degradation kinetics and GFP fluorescence intensity when measured across a large number of individual cells. This work illustrates the application of quantitative, live cell microscopy using a promoter-driven GFP reporter cell line to measure the dynamics of single cell gene expression activity. A large number of signaling pathways have been implicated in the activation of tenascin-C gene transcription. Our results suggest that tenascin-C expression is, at least in part, directly coupled to proliferation and cell cycle progression. 1 National Institute of Standards and Technology, Gaithersburg MD
2ATCC, Manassas, VA
3SAIC, Arlington, VA
Marcus John Tindall (University of Oxford) Spatiotemporal modelling of intracellular signalling in Rhodobacter sphaeroidess
Abstract: Joint work with S.L. Porter2, P.K. Maini1,3, J.P. Armitage2,3. The role that spatial protein localisation plays in altering the expression of flagellar motor driving proteins in bacterial chemotaxis has to date largely been ignored. The work presented here focuses on a mathematical spatiotemporal reaction-diffusion model of signal transduction developed to describe phosphotransfer in Rhodobacter sphaeroides. The mathematical model is used to understand the role that spatial protein localisation has on affecting the motor protein expression and the connection between the cytoplasmic and receptor clusters in describing the overall bacterial response. 1 Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB.
2Department of Biochemistry, Microbiology Unit, University of Oxford, South Parks Road, Oxford, OX1 3QU.
3Oxford Centre for Integrative Systems Biology, Department of Biochemistry, University of Oxford, South Parks Road, Oxford, OX1 3QU.
Lev S. Tsimring (University of California, San Diego) Stochastic oscillations in small genetic networks
Abstract: One of the defining characteristics of life is the ability to keep time, which organisms often achieve by using internal genetic "clocks" to govern fundamental cellular behavior. While the gene networks that produce oscillatory expression signals are typically quite elaborate, certain recurring network motifs are often found at the core of these biological clocks. In this lecture, I will describe our recent experimental and theoretical work on small genetic networks exhibiting oscillatory behavior. One common motif which may lead to oscillations is delayed auto-repression. We constructed synthetic oscillators based on this design principle, and observed robust and tunable oscillations both in bacteria and yeast. Since genetic systems typically involve small number of reacting components, intrinsic fluctuations play an important role in the dynamics. I will introduce theoretical and computational tools which can be used for modeling stochastic dynamics of small genetic networks.
Yuhai Tu (IBM) From molecule to behavior: E. coli’s memory, computation and taxis
Abstract: In this talk, I will present our recent work in trying to understand bacterial chemotaxis (bacteria’s ability to sense and track chemical gradient) by using a quantitative modeling approach. Based on molecular level knowledge of the E. coli chemotaxis pathway, we propose a simple model for bacterial chemotaxis and use it to address several interesting, important system-level questions: 1) What kind of computation does a E. coli cell perform in response to complex time-varying stimuli? 2) What kind of memory does E. coli have? How long does it take the cell to forget? 3) How does the cell use its memory and computation capability to sense and respond to a minute chemical gradient (food or poison) among a wide range of background.
Melissa Vellela (University of Washington) Stochastic modeling of bistable chemical systems: Schlogl's model
Abstract: When describing chemical systems in a nonequilibrium steady state, striking differences arise in the predictions between deterministic and stochastic models. Using a classic model first introduced by Schlogl, we study the steady state behaviors of a one dimensional, open system that exhibits bistability. The definitions of thermodynamic quantities, such as flux, chemical potential, and entropy production rate are compared across the two types of models. The stochastic model allows for jumping between the two stable steady states which are separated by an unstable steady state in the deterministic model. The transition rates and exponentially small eigenvalue associated with this jumping are investigated and calculated numerically. Understanding the behavior of the stochastic steady state directly from the master equation is important because even widely used approximations such as Fokker-Planck can be incorrect, as is shown for this example.
Rajitha Vuppula (Indian Institute of Technology-Bombay) Chemotaxis of E. coli towards glucose
Abstract: Joint work with Mahesh S. Tirumkudulu and K.V. Venkatesh We describe a technique to create stable glucose gradients without requiring any fluid flow. The gradients are measured in both, space and time, using fluorescent glucose. We quantify the chemotaxis of E. coli by measuring the diffusivity and drift velocity of individual bacteria at varying glucose gradients.
Yu-li Wang (University of Massachusetts Medical School, Worcester Campus) Adherent cells as a mechanical device - probing the forces and understanding the regulatory circuit
Abstract: We have applied new experimental and computational approaches to understand the mechanical events of adherent cells. While the extensive use of flexible substrates has lead to excellent understanding of traction forces, introduction of long polymers into the cytoplasm has started to shed light on weak gradients of forces generated by the cortex. In addition, a top-down mathematical model has been developed to simulate the control circuit that coordinates protrusions and retractions. The model is capable of generating experimentally measurable parameters, which in turn allows the use of optimization algorithms to match the model with observations, and to provide insights into how a unified feedback mechanism might generate a wide range of behaviors.
Alissa Weaver (Vanderbilt University) Computational modeling of invadopodia-ECM interactions
Abstract: Invadopodia are subcellular protrusive structures associated with sites of extracellular matrix (ECM) degradation. Little is known about the regulation of invadopodia functions by ECM properties. I will discuss a joint experimental-computational study in which we have modeled and tested the regulation of invadopodia formation and function by crosslinked gelatin and collagen substrates. We find that crosslinking inhibits degradation and penetration of invadopodia in dense substrates, such as gelatin, but not in loose collagen matrices. These results provide a framework for consideration of diverse types of matrices that invasive cells may experience in vivo.
Cornelius Weijer (University of Dundee) Chemotactic cell movement during Dictyostelium development and chick gastrulation
Abstract: We investigate the molecular mechanisms by which cells produce and detect chemotactic signals and translate this information in directed coordinated movement up or down chemical gradients in the social amoebae Dictyostelium discoideum, and during gastrulation in the chick embryo. In Dictyostelium starvation for food induces the aggregation of up to hundreds of thousands of individual amoebae into a multi-cellular aggregate. During aggregation the cells differentiate into several distinct celltypes, which sort out to form a migrating slug, which after a variable period of migration transforms into a fruiting body consisting of a stalk supporting a mass of spores. Experiments show that chemotactic cell migration in all stages of development is controlled by propagating waves of the chemo-attractant cAMP. At present we concentrate on investigation of the mechanisms that drive chemotactic cell sorting which results in slug formation. We use quantitative imaging techniques to investigate cell type specific differences in signal transduction dynamics, polarised activation of the actin-myosin cytoskeleton and force generation that drive cell sorting. Gastrulation in the chick embryo starts with the occurring of extensive cell flows that result in the formation of the primitive streak, a structure through which the mesoderm and endoderm precursor cells ingress to take up their correct positions in the embryo. We are tracking the in-vivo migration of these cells during streak formation and after their ingression through the primitive streak to gain insight in the mechanisms that drive these cell movements. Our current hypothesis is that formation of the primitive streak as well as the movement of the mesoderm cells after their ingression through the streak is controlled by a combination of attractive and repulsive guidance cues, delivered at least in part by members of the FGF, VEGF, PDGF and Wnt families of signalling molecules.
Darren James Wilkinson (University of Newcastle upon Tyne) Bayesian inference for stochastic intracellular reaction network models
Abstract: This talk will provide an overview of computationally intensive methods for conducting Bayesian inference for the rate constants of stochastic kinetic intracellular reaction network models using single-cell time course data. Inference for the true Markov jump process is extremely challenging in realistic scenarios, so the true model will be replaced by a diffusion approximation, known in this context as the Chemical Langevin Equation (CLE). Inference for the CLE is also challenging, but the development of effective algorithms is possible, and turns out to be extremely effective, even in scenarios where one would expect the diffusion approximation to break down.
Ruth J. Williams (University of California, San Diego) Part II: Homotopy methods for counting reaction network equilibria
Abstract: Based on joint work with G. Craciun and J. W. Helton. Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model.
Yuan Xiong (Johns Hopkins University) Automated characterization of cell shape changes during amoeboid motility
Abstract: The ability of a cell to change shape is crucial for the proper function of many cellular processes, such as chemotaxis. Traditionally, cell motility has been characterized by a number of different parameters, determined either by the position of the cell's centroid as it migrates, or by limited aspects of the cell shape such as perimeter, area roundness and body orientation. These parameters primarily provide global information about chemotaxis and chemoattractant-induced cell shape changes. They are insufficient to distinguish cell strains based on local morphological information, such as pseudopodial protrusions, that typify amoeboid motility. When the activity of pseudopods has been described, the protrusions and retractions have been identified and outlined mostly manually. In addition to being highly time consuming, these manual methods have the drawback that they are based on subjective judgments. Here we describe a series of automated methods used to characterize amoeboid locomotion based on the skeleton of a planar shape. We demonstrate that the skeleton can be used to identify pseudopods in microscopic images of moving cells. Moreover, the time-varying evolution of the skeleton can be used to capture the dynamic nature of the pseudopodial protrusions and retractions
Richard Yamada (University of Michigan) Biochemical and network modeling of the mammalian suprachiasmatic nucleus
Abstract: The Supra-Chiasmatic Nucleus (SCN) is the central oscillator that keeps time in all mammalian organisms. Central to understanding the circadian rhythms that these oscillators generate are the multitude of interacting genes and proteins, in addition to the complex interactions of coupled SCN cells. In recent year, quantitative modelling has emerged as an additional tool complimenting experimental techniques in the study of circadian rhythms. In this poster, we discuss a detailed mathematical model for circadian timekeeping within the SCN. Our proposed model consists of a large population of SCN neurons, with each neuron containing a network of biochemical reactions involving the core circadian components. Central to our work is the determination of the model’s unkown parameters, which were obtained from comparing the model’s output to experimental data. From these estimated parameters, additional experimental test of the model are proposed. Our studies highlight the importance of low numbers of molecules of clock proteins, and how this fact addects the accuracy of circadian timekeeping.
John Yin (University of Wisconsin) Models and measures of virus growth and infection spread
Abstract: When a virus infects a living cell it directs the biosynthetic resources of the cell toward transcription and translation of viral proteins, replication of viral genomes, assembly of virus particles, and release of hundreds to thousands of progeny virus particles to the extracellular environment. For well-characterized viruses one may begin to build kinetic models that predict virus growth behavior based on the dynamics of the underlying molecular processes within the infected cell. Recent experimental study of single BHK cells infected by single particles of vesicular stomatitis virus, a virus that encodes only five genes, reveal a broad distribution of virus productivity. Viral genetic variation and host-cell heterogeneity are unable to fully account for the broad growth behavior. A better understanding of these experiments may follow from stochastic modeling of virus growth.
Shan Zhao (University of Alabama) The minimal molecular surface
Abstract: We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy minimization occurs naturally to stabilize the system, and leads to an MMS separating the macromolecule from the solvent. For a given set of atomic constraints (as obstacles), the MMS is defined as one whose mean curvature vanishes away from the obstacles. Based on the theory of differential geometry, an iterative procedure is proposed to compute the MMS via the mean curvature minimization of molecular hypersurface functions. Extensive numerical experiments, including those with internal and open cavities, are carried out to demonstrate the proposed concept and algorithms. Comparison is given to the molecular surface. Unlike the molecular surface, the proposed MMS is typically free of singularities. The application of the MMS to the electrostatic analysis is considered for a set of twenty six proteins.
Xiaoming Zheng (University of Michigan) A Multiscale model of endothelial cell migration, proliferation and maturation in angiogenesis
Abstract: Joint work with Trachette Jackson (Mathematics Department, University of Michigan). A new multiscale mathematical model of angiogenesis is developed to quantify the relative roles of cell quiescence, proliferation and migration. Migration is assumed to be the primary event of sprouting, and the governing equation is derived based on cellular mechanics. The extension of the vessel, however, is restricted by the supply of endothelial cells, which is dominated by the proliferation. Although all cells are capable of proliferating, experimental observations often conclude that the proliferative activity is concentrated in the region proximal to the leading edge. In order to capture this phenomenon, we introduce the concept of maturation level, which is modulated by angiopoietins, to describe a quiescent phenotype of endothelial cells. All of these features are combined into a multiscale model of vessel extension in angiogenesis, including vessel anastomosis and branching. Relations between extension and proliferation are investigated, and comparisons to rat cornea experiments are made.
Dietmar Bernhard Ölz (Universität Wien) From the curve straightening flow in the plane to a model for the Lamellipodial Actin-cytoskeleton
Abstract: The presentation deals with the modelling approach on the Actin-cytoskeleton presented too in the talk of C. Schmeiser. In the first part of the talk we derive the model in a step by step way starting form the curve straightening flow of planar open curves generated by the Kirchhoff bending energy. We show numerical simulations and present a local in time existence result of solutions and regularity results. In the second part we go back to the curve straightening flow and formulate the governing equations in terms of the indicatrix and a scalar Lagrange multiplier function. We prove existence and (improved) regularity of solutions. We compute the energy dissipation, prove its coercivity and conclude the exponential decay of the energy.
Visitors in Residence
Jonathan B. Alberts University of Washington 5/26/2008 - 5/30/2008
Claudio Altafini International School for Advanced Studies (SISSA/ISAS) 4/15/2008 - 5/15/2008
David F. Anderson University of Wisconsin 5/10/2008 - 5/14/2008
Ping Ao University of Washington 5/10/2008 - 5/13/2008
Douglas N. Arnold University of Minnesota 7/15/2001 - 6/30/2008
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2009
Paul Atzberger University of California 5/26/2008 - 5/30/2008
Daniel J. Bates University of Minnesota 9/1/2006 - 8/31/2008
John Baxter University of Minnesota 8/1/2007 - 4/1/2009
Banu Baydil Rensselaer Polytechnic Institute 3/1/2008 - 6/30/2008
Yermal Sujeet Bhat University of Minnesota 9/1/2006 - 8/31/2008
Tracy Bibelnieks Augsburg College 5/27/2008 - 5/30/2008
Lisa Bishop University of Washington 5/10/2008 - 5/13/2008
Khalid Boushaba Iowa State University 1/15/2008 - 6/30/2008
Maury Bramson University of Minnesota 5/10/2008 - 5/13/2008
Dennis Bray University of Cambridge 5/1/2008 - 5/30/2008
Mónica F. Bugallo SUNY 5/10/2008 - 5/13/2008
Don Button University of Alaska 5/11/2008 - 5/12/2008
Maria-Carme T. Calderer University of Minnesota 5/11/2008 - 5/13/2008
Maria-Carme T. Calderer University of Minnesota 5/27/2008 - 5/30/2008
Hannah Callender University of Minnesota 9/1/2007 - 8/31/2009
Yang Cao Virginia Polytechnic Institute and State University 5/10/2008 - 5/13/2008
Yang Cao Virginia Polytechnic Institute and State University 5/26/2008 - 5/30/2008
Anders E. Carlsson Washington University 5/26/2008 - 5/30/2008
Teng Chen University of Central Florida 5/10/2008 - 5/14/2008
Lauren Maressa Childs Cornell University 5/10/2008 - 5/14/2008
Gregory S. Chirikjian Johns Hopkins University 5/25/2008 - 5/30/2008
Yung-Sze Choi University of Connecticut 4/1/2008 - 5/31/2008
Ioana Cipcigan University of Maryland Baltimore County 5/10/2008 - 5/13/2008
Duncan J. Clarke University of Minnesota 5/20/2008 - 5/20/2008
Philippe Cluzel University of Chicago 5/29/2008 - 5/30/2008
John S. Condeelis Albert Einstein College of Medicine 5/26/2008 - 5/30/2008
Ludovica Cecilia Cotta-Ramusino University of Minnesota 10/1/2007 - 8/30/2009
Gheorghe Craciun University of Wisconsin 5/10/2008 - 5/13/2008
Gaudenz Danuser Scripps Research Institute 5/26/2008 - 5/31/2008
Lance Davidson University of Pittsburgh 5/26/2008 - 5/30/2008
Adriana Dawes University of Washington 5/26/2008 - 5/30/2008
Micah Dembo Boston University 5/26/2008 - 5/30/2008
Anilkumar Devarapu University of Louisville 5/11/2008 - 5/14/2008
Lee DeVille University of Illinois at Urbana-Champaign 5/10/2008 - 5/13/2008
Rich Dickinson University of Florida 5/26/2008 - 5/30/2008
Ton Dieker IBM 5/11/2008 - 5/13/2008
Kequan Ding Chinese Academy of Sciences 4/15/2008 - 5/31/2008
Petar M. Djuric SUNY 5/10/2008 - 5/13/2008
Olivier Dubois University of Minnesota 9/3/2007 - 8/31/2009
Leah Edelstein-Keshet University of British Columbia 5/29/2008 - 5/30/2008
Walid Fakhouri Michigan State University 5/10/2008 - 5/14/2008
Martin Falcke Hahn-Meitner-Institut für Kernforschung (Nuclear Research) Berlin GmbH 5/26/2008 - 5/31/2008
Sergei Fedotov University of Manchester 5/5/2008 - 6/4/2008
Daniel Fletcher University of California 5/26/2008 - 5/30/2008
Christodoulos A. Floudas Princeton University 4/1/2008 - 6/30/2008
Henrik Flyvbjerg Technical University of Denmark 5/26/2008 - 5/30/2008
John Fricks Pennsylvania State University 5/10/2008 - 5/14/2008
Arnab Ganguly University of Wisconsin 5/10/2008 - 5/13/2008
Margaret Gardel University of Chicago 5/26/2008 - 5/30/2008
Melissa K. Gardner University of Minnesota 5/27/2008 - 5/30/2008
Peter W. Glynn Stanford University 5/11/2008 - 5/13/2008
Nir Shachna Gov Weizmann Institute of Science 5/26/2008 - 5/30/2008
Jason E. Gower University of Minnesota 9/1/2006 - 8/31/2008
Paula Grajdeanu Ohio State University 5/10/2008 - 5/14/2008
Robert Guy University of California 3/24/2008 - 6/24/2008
Peter J. Haas IBM Research Division 5/11/2008 - 5/13/2008
Esfandiar Haghverdi Indiana University 1/2/2008 - 6/30/2008
Adam Miklos Halasz University of Pennsylvania 5/10/2008 - 5/14/2008
Mark Harris Vanderbilt University 5/26/2008 - 5/31/2008
Dirk Hartmann Ruprecht-Karls-Universität Heidelberg 5/22/2008 - 6/21/2008
Thomas Hays University of Minnesota 5/27/2008 - 5/30/2008
Gerald L. Hazelbauer University of Missouri 5/26/2008 - 5/30/2008
David Heine Corning 5/26/2008 - 5/30/2008
Milena Hering University of Minnesota 9/1/2006 - 8/31/2008
Anthony Hill University of Minnesota 5/11/2008 - 5/13/2008
Thomas Hillen University of Alberta 4/27/2008 - 5/10/2008
Peter Hinow University of Minnesota 9/1/2007 - 8/31/2009
Rick Horwitz University of Virginia 5/26/2008 - 5/29/2008
Martin Howard John Innes Centre 5/24/2008 - 5/30/2008
Bo Hu Center for Theoretical Biological Physics, UCSD 5/26/2008 - 5/31/2008
DiAnna Lynn Hynds Texas Woman's University 5/26/2008 - 5/31/2008
Pablo A. Iglesias Johns Hopkins University 5/26/2008 - 5/30/2008
Ken Jacobson University of North Carolina 5/26/2008 - 5/30/2008
Richard D. James University of Minnesota 9/4/2007 - 6/30/2008
Imre M. Jánosi Eötvös Loránd University (ELTE) 2/1/2008 - 6/30/2008
Junhwan Jeon Vanderbilt University 5/26/2008 - 5/30/2008
Tiefeng Jiang University of Minnesota 9/1/2007 - 6/30/2008
Hye-Won Kang University of Wisconsin 5/11/2008 - 5/14/2008
Yiannis N. Kaznessis University of Minnesota 5/10/2008 - 5/13/2008
Eric Kim Vanderbilt University 5/26/2008 - 5/31/2008
Kyung Hyuk Kim University of Washington 5/10/2008 - 5/13/2008
Debra Knisley East Tennessee State University 8/17/2007 - 6/1/2008
Dmitry A. Kondrashov University of Chicago 5/9/2008 - 5/13/2008
Samuel Kou Harvard University 5/10/2008 - 5/13/2008
Youri A. Koutoyants Université du Maine 5/10/2008 - 5/14/2008
Michael M. Kozlov Tel Aviv University 5/26/2008 - 5/31/2008
Peter R. Kramer Rensselaer Polytechnic Institute 1/8/2008 - 6/30/2008
Daniel Kroll North Dakota State University 5/27/2008 - 5/31/2008
Thomas G. Kurtz University of Wisconsin 5/10/2008 - 5/13/2008
Yueheng Lan University of California 5/10/2008 - 5/13/2008
Lorene Lanier University of Minnesota 5/27/2008 - 5/30/2008
Juan Latorre Rensselaer Polytechnic Institute 1/10/2008 - 6/30/2008
Chang Hyeong Lee Worcester Polytechnic Institute 5/6/2008 - 5/13/2008
Juliet Lee University of Connecticut 5/26/2008 - 5/30/2008
Pilhwa Lee University of Colorado 5/26/2008 - 5/30/2008
Howard A. Levine Iowa State University 5/13/2008 - 5/16/2008
Anton Leykin University of Minnesota 8/16/2006 - 8/15/2008
James C. Liao University of California 5/12/2008 - 5/13/2008
Karen Lipkow University of Cambridge 5/24/2008 - 5/31/2008
Chun Liu Pennsylvania State University 4/28/2008 - 5/3/2008
Di Liu Michigan State University 5/10/2008 - 5/13/2008
Hailiang Liu Iowa State University 5/11/2008 - 5/13/2008
Wolfgang Losert University of Maryland 5/27/2008 - 5/29/2008
Roger Y. Lui Worcester Polytechnic Institute 9/1/2007 - 6/30/2008
Laura Lurati University of Minnesota 9/1/2006 - 8/31/2008
Dionisios Margetis University of Maryland 5/26/2008 - 5/31/2008
M. David Marks University of Minnesota 5/11/2008 - 5/13/2008
Bonnie Marsick University of Minnesota 5/27/2008 - 5/30/2008
Scott McKinley Duke University 5/10/2008 - 5/14/2008
Bence Melykuti University of Oxford 5/10/2008 - 5/14/2008
Vicenc Mendez Autonomous University of Barcelona 5/1/2008 - 5/31/2008
Tobias Meyer Stanford University 5/26/2008 - 5/29/2008
Paul Milewski University of Wisconsin 5/26/2008 - 5/30/2008
Ezra Miller University of Minnesota 9/1/2007 - 6/30/2008
Hitesh Mistry University of Dundee 5/10/2008 - 5/14/2008
Alex Mogilner University of California 5/26/2008 - 6/1/2008
Michael Monine Los Alamos National Laboratory 5/10/2008 - 5/13/2008
Denise Montell Johns Hopkins University 5/26/2008 - 5/30/2008
Yoichiro Mori University of British Columbia 5/26/2008 - 6/1/2008
Ambarish Nag Los Alamos National Laboratory 5/10/2008 - 5/14/2008
Timothy Newman Arizona State University 9/1/2007 - 6/30/2008
Duane Nykamp University of Minnesota 9/1/2007 - 6/30/2008
David Odde University of Minnesota 1/9/2008 - 6/30/2008
James Oliver University of Oxford 5/24/2008 - 5/31/2008
Dietmar Bernhard Ölz Universität Wien 5/25/2008 - 6/8/2008
Hans G. Othmer University of Minnesota 9/1/2007 - 6/30/2008
John Sandy Parkinson University of Utah 5/27/2008 - 5/30/2008
Johan Paulsson Harvard Medical School 5/11/2008 - 5/13/2008
Bobby Philip Los Alamos National Laboratory 4/16/2008 - 5/30/2008
Jonathan Popko University of Minnesota 5/27/2008 - 5/30/2008
Lea Popovic Concordia University 5/10/2008 - 5/13/2008
Mary Porter University of Minnesota 5/27/2008 - 5/30/2008
Alka A. Potdar Vanderbilt University 5/26/2008 - 5/30/2008
Aravind R. Rammohan Corning 5/26/2008 - 5/30/2008
Chris Rao University of Illinois at Urbana-Champaign 5/26/2008 - 5/30/2008
Muruhan Rathinam University of Maryland Baltimore County 5/10/2008 - 5/13/2008
Eric J. Rawdon University of St. Thomas 1/10/2008 - 6/30/2008
Michael C. Reed Duke University 5/11/2008 - 5/13/2008
Grzegorz A. Rempala University of Louisville 5/11/2008 - 5/14/2008
Erin Rericha University of Maryland 5/26/2008 - 5/30/2008
Alexander Roitershtein University of British Columbia 5/10/2008 - 5/14/2008
Howard Salis University of California 5/10/2008 - 5/13/2008
Sebastian Ambrose Sandersius Arizona State University 5/1/2008 - 6/14/2008
Fadil Santosa University of Minnesota 4/23/2008 - 5/2/2008
Jeffery G. Saven University of Pennsylvania 3/19/2008 - 6/10/2008
Christian Schmeiser Universität Wien 5/26/2008 - 5/31/2008
Deena Schmidt University of Minnesota 9/1/2007 - 8/31/2009
Casey Schneider-Mizell University of Michigan 5/26/2008 - 5/31/2008
Sven A. Sewitz University of Cambridge 5/24/2008 - 5/31/2008
Chehrzad Shakiban University of Minnesota 9/1/2006 - 8/31/2008
Shagi-Di Shih University of Wyoming 5/26/2008 - 5/31/2008
Julie Simons University of Wisconsin 5/26/2008 - 5/30/2008
Vassilios Sotiropoulos University of Minnesota 5/11/2008 - 5/13/2008
Rishi Srivastava University of Wisconsin 5/10/2008 - 5/14/2008
Andrew Stein University of Minnesota 9/1/2007 - 8/31/2009
Magdalena Stolarska University of St. Thomas 5/27/2008 - 5/30/2008
Sean Sun Johns Hopkins University 5/26/2008 - 5/30/2008
Vladimir Sverak University of Minnesota 9/1/2007 - 6/30/2008
Tatyana Svitkina University of Pennsylvania 5/26/2008 - 5/30/2008
Csilla Szabo Rensselaer Polytechnic Institute 5/26/2008 - 5/31/2008
David Tello Arizona State University 5/10/2008 - 5/14/2008
Julie A. Theriot Stanford University 5/26/2008 - 5/30/2008
Marcus John Tindall University of Oxford 5/26/2008 - 5/31/2008
Mahesh Tirumkudulu Indian Institute of Technology-Bombay 5/25/2008 - 5/31/2008
Margaret A Titus University of Minnesota 5/27/2008 - 5/30/2008
Lev S. Tsimring University of California, San Diego 5/10/2008 - 5/13/2008
Yuhai Tu IBM 5/27/2008 - 5/30/2008
Erkan Tüzel University of Minnesota 9/1/2007 - 8/31/2009
Melissa Vellela University of Washington 5/10/2008 - 5/13/2008
K.V. Venkatesh Indian Institute of Technology-Bombay 5/25/2008 - 5/31/2008
Jorge Vinals McGill University 5/8/2008 - 5/14/2008
Rajitha Vuppula Indian Institute of Technology-Bombay 5/26/2008 - 5/30/2008
Jin Wang SUNY 5/11/2008 - 5/14/2008
Jin Wang SUNY 5/26/2008 - 5/30/2008
Yu-li Wang University of Massachusetts Medical School, Worcester Campus 5/26/2008 - 5/30/2008
Zhian Wang University of Minnesota 9/1/2007 - 8/31/2009
Alissa Weaver Vanderbilt University 5/26/2008 - 5/30/2008
Cornelius Weijer University of Dundee 5/26/2008 - 5/31/2008
Hans Weinberger University of Minnesota 2/13/2008 - 6/30/2008
Darren James Wilkinson University of Newcastle upon Tyne 5/10/2008 - 5/13/2008
Ruth J. Williams University of California, San Diego 5/10/2008 - 5/13/2008
Charles Wolgemuth University of Connecticut Health Center 5/26/2008 - 5/30/2008
Zhijun Wu Iowa State University 9/4/2007 - 6/1/2008
Yuan Xiong Johns Hopkins University 5/26/2008 - 5/30/2008
Chuan Xue University of Minnesota 5/27/2008 - 5/30/2008
Richard Yamada University of Michigan 5/10/2008 - 5/14/2008
Richard Yamada University of Michigan 5/25/2008 - 5/30/2008
John Yin University of Wisconsin 5/10/2008 - 5/13/2008
Hongchao Zhang University of Minnesota 9/1/2006 - 8/31/2008
Zhigang Zhang University of Houston-Downtown 5/10/2008 - 5/14/2008
Shan Zhao University of Alabama 5/26/2008 - 5/29/2008
Xiaoming Zheng University of Michigan 5/26/2008 - 5/30/2008
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
3M, Arizona State University, Boeing, Carnegie Mellon University, Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Schlumberger-Doll Research, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute